The rapid deployment of autonomous AI agents across enterprise, healthcare, and safety-critical environments has created a fundamental governance gap. Existing approaches, runtime guardrails, training-time alignment, and post-hoc auditing treat governance as an external constraint rather than an internalized behavioral principle, leaving agents vulnerable to unsafe and irreversible actions. We address this gap by drawing on how humans self-govern naturally: before acting, humans engage deliberate cognitive processes grounded in executive function, inhibitory control, and internalized organizational rules to evaluate whether an intended action is permissible, requires modification, or demands escalation. This paper proposes a neurocognitive governance framework that formally maps this human self-governance process to LLM-driven agent reasoning, establishing a structural parallel between the human brain and the large language model as the cognitive core of an agent. We formalize a Pre-Action Governance Reasoning Loop (PAGRL) in which agents consult a four-layer governance rule set: global, workflow-specific, agent-specific, and situational before every consequential action, mirroring how human organizations structure compliance hierarchies across enterprise, department, and role levels. Implemented on a production-grade retail supply chain workflow, the framework achieves 95% compliance accuracy and zero false escalations to human oversight, demonstrating that embedding governance into agent reasoning produces more consistent, explainable, and auditable compliance than external enforcement. This work offers a principled foundation for autonomous AI agents that govern themselves the way humans do: not because rules are imposed upon them, but because deliberation is embedded in how they think.